An Extended Exploration to the Epidemic Containment Game

Abstract

The epidemic containment game is a formulation to describe voluntary vaccination behaviors before epidemic spreading. This game relies on the characterization of the susceptible-infected- susceptible (SIS) model in terms of the spectral radius of the network. Existing researches showed that finding the worst Nash Equilibrium (NE) is NP-hard and used a heuristic algorithm called Low Degree (LDG) to estimate the maximum social cost under the worst NE (Max NE cost). By comparing the results of the LDG algorithm and exhaustive search, we found the LDG algorithm cannot estimate Max NE cost well, thus, we proposed a new neighbor information based algorithm to estimate Max NE cost in this paper. Moreover, we discussed Stackelberg strategies in which some nodes are secured first by a leader, then other agents choose their strategies voluntarily. We found the target (TAR) strategy is effective to reduce Max NE cost in a scale- free network when T is large and useless when T is low (T is the ratio of the recovery rate to the transmission rate in the SIS model). Moreover, we found that a lot of nodes with small degrees are secured voluntarily under the TAR strategy when T is low, which leads to high Max NE cost. At last, we proposed a new greedy algorithm to select nodes secured first, which can reduce Max NE cost when T is low.